Question

find the second derivative for 4x^3/2
its quite simple but i keep having problems with fractions

Answer 1

\(\large y = 4x^{\frac{3}{2}} \)

\(\large y' = \dfrac{3}{2}(4)x^{\frac{1}{2}} = 6x^{\frac{1}{2}} \)

\(\large y'' = (6x^{\frac{1}{2}})' = \dfrac{1}{2}(6) {x^{-\frac{1}{2}}} = 3{x^{-\frac{1}{2}}}
= \dfrac{3}{\sqrt{x}} \)